Getting and keeping your kids interested in BJJ can be tricky, but there are tricks to keep them interested. Mostly though, the trick is being involved in the right way. By this I mean don't be a dick.
We all know the dads and moms who want to bully their kids into doing what they want them to do. Coercing is one thing, bullying is something all together different. Telling your kid he/she is a wimp for example, (I've actually heard this one) would be a form of bullying. There are enough bullies in this world, please do not create any more.
I think a list of dos and don’ts would be helpful...
Do: Take time to wrestle with your kids at least a few times a week
Don't: Keep correcting all of their mistakes
Do: Encourage and praise the things they do right
Don't: Make them wrestle their siblings, this is a recipe for disaster until they are old enough to understand what they are doing
Do: Encourage them about their progress in front of others. Pro tip - this works even better if they overhear you talking about them when you think they aren't there
Don't: Over coach your kids, especially when they are being coached by a professional
Do: Encourage your kids to do their best and let them know you're proud of them.
Don't: Pay too much attention to winning
Do: Encourage learning and sportsmanship
You get the idea. All parents want their kids to do well, but inadvertently discouraging them won't help any. If you are wrestling or helping them with their moves, make sure you tell them “good job” even if they aren't doing it right but then gently correct and tell them this is even better.